FWIW,
That rethreading set that Summit is selling IS the one made by Lang. They just have their own labeling on it.
If you look at the one on Amazon and the one at Summit, you can compare the 2. It even looks to be in the same blow molded container, with the black oxide parts having swapped position with the silver colored ones.
About COO information:
A COO is technically a Certificate Of Origin, (which is REQUIRED by US Customs on IMPORTED goods), although many people use it to mean Country of Origin, which is still essentially correct but using it THAT way leads to confusion about why it may be there on some products and not on other, often very similar ones.
ONLY when a product is IMPORTED, and is packaged for retail sale, is the final customer required (technically-and sometimes this is ignored) to know the Country of Origin and such information is ncluded in some manner-EITHER on the packaging or somewhere the item itself. (And there ARE specific exceptions to this requirement.) The vast majority of NON imported products do not require Country of Origin labelling to be done, although it often is done for marketing purposes, ("Made in USA" does still help sell some products) and sometimes done to meet the demands of specific entities/organizations/etc. both in the governmental sector and the civil.